ON BOSE-CHAUDHURI-HOCQUENGHEM CODES OVER GF (Q).
ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB
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Two related aspects of the BCH codes have been investigated. The problems are 1 to have a better knowledge concerning their minimum distances, and 2 to find decoding methods not limited by the BCH bounds. A theory is presented which enables one to determine if a particular BCH code has minimum distance larger than its BCH bound. The derivation of this new theory is based on the Mattson-Solomon approach. The new results are easy to apply as illustrated by several examples. They are applicable to many codes including the well-known Golay 11,6 code over GF3. A general algebraic full-power decoding method is outlined. In addition, two different methods are presented for the two special cases 1 the decoding of the two Golay perfect codes to its full error-correcting capability, and 2 the decoding of concactonated codes. All decoding methods are found to be quite practical. Author